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of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationTue, 27 May 2008 04:50:41 -0600
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/May/27/t1211885503tqqyx73r31a7tu0.htm/, Retrieved Mon, 20 May 2024 00:07:52 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=13324, Retrieved Mon, 20 May 2024 00:07:52 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact209
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Classical Decomposition] [oef 9nr 1 decompo...] [2008-05-24 21:57:19] [6d22fa1dc30661eaeb7c69c42abd0d0e]
- RMPD    [Exponential Smoothing] [oef 10, exponenti...] [2008-05-27 10:50:41] [7447f24868087d6abebd401b46b50271] [Current]
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Post a new message
Dataseries X:
209
214
265
290
287
270
263
265
252
281
259
312
275
250
312
331
256
247
291
318
296
291
313
311
273
258
361
391
446
433
449
479
460
466
410
415
382
409
496
471
488
584
610
684
626
580
444
552
473
431
513
467
470
455
406
424
406
373
332
310
301
296
333
374
422
424
341
216
319
383
360
400




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 5 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13324&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]5 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13324&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13324&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time5 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.912381994071253
beta0
gamma0

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.912381994071253 \tabularnewline
beta & 0 \tabularnewline
gamma & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13324&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.912381994071253[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13324&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13324&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.912381994071253
beta0
gamma0







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
326521451
4290260.53148169763429.4685183023661
5287287.418027188672-0.418027188671942
6270287.036626708695-17.0366267086955
7263271.492715259968-8.49271525996835
8265263.7441147759991.25588522400096
9252264.889961840998-12.8899618409977
10281253.12939275300627.8706072469942
11259278.558032968995-19.5580329689951
12312260.71363584863251.286364151368
13275307.506391041722-32.5063910417215
14250277.848145163016-27.8481451630157
15312252.43999894799859.5600010520023
16331306.78147147471024.2185285252905
17256328.878020824086-72.8780208240856
18247262.38542686064-15.3854268606401
19291248.34804042189242.6519595781081
20318287.26292035281330.7370796471873
21296315.30687837324-19.3068783732404
22291297.691630183772-6.69163018377213
23313291.58630729311521.4136927068852
24311311.123774945452-0.123774945451771
25273311.010844913904-38.0108449139044
26258276.330434435023-18.3304344350232
27361259.606076113004101.393923886996
28391352.1160665757338.8839334242696
29446387.59306729069958.4069327093006
30433440.882501023597-7.8825010235966
31449433.69064902141915.3093509785812
32479447.65862519519331.3413748048066
33460476.253931236537-16.2539312365374
34466461.4241370434484.57586295655165
35410465.599072012344-55.5990720123438
36415414.871479821210.128520178789643
37382414.988739318213-32.9887393182129
38409384.89040755716524.109592442835
39496406.88756558640489.112434413596
40471488.192146193225-17.1921461932245
41488472.50634156708615.4936584329142
42584486.64247654356797.357523456433
43610575.46972793258634.5302720674139
44684606.97452641727677.0254735827239
45626677.251181598964-51.2511815989643
46580630.490526333193-50.4905263331933
47444584.423879235607-140.423879235607
48552456.30366028340395.696339716597
49473543.615277539352-70.6152775393518
50431479.187169806103-48.187169806103
51513435.22206372976177.7779362702393
52467506.185252318748-39.1852523187485
53470470.433333669984-0.43333366998354
54455470.037967832066-15.0379678320658
55406456.317596754666-50.3175967546663
56424410.40872749077113.5912725092294
57406422.809159804707-16.8091598047072
58373407.472785063426-34.4727850634261
59332376.020436686068-44.0204366860677
60310335.856982882546-25.8569828825459
61301312.265537279502-11.2655372795024
62296301.987063912146-5.98706391214597
63333296.5245746013536.4754253986498
64374329.80409596116844.1959040388325
65422370.12764301789951.8723569821008
66424417.4550475184046.54495248159577
67341423.426544314664-82.4265443146642
68216348.222049448448-132.222049448448
69319227.58503231248591.4149676875148
70383310.99040281917972.0095971808209
71360376.690662687284-16.6906626872842
72400361.46240258228938.5375974177108

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 265 & 214 & 51 \tabularnewline
4 & 290 & 260.531481697634 & 29.4685183023661 \tabularnewline
5 & 287 & 287.418027188672 & -0.418027188671942 \tabularnewline
6 & 270 & 287.036626708695 & -17.0366267086955 \tabularnewline
7 & 263 & 271.492715259968 & -8.49271525996835 \tabularnewline
8 & 265 & 263.744114775999 & 1.25588522400096 \tabularnewline
9 & 252 & 264.889961840998 & -12.8899618409977 \tabularnewline
10 & 281 & 253.129392753006 & 27.8706072469942 \tabularnewline
11 & 259 & 278.558032968995 & -19.5580329689951 \tabularnewline
12 & 312 & 260.713635848632 & 51.286364151368 \tabularnewline
13 & 275 & 307.506391041722 & -32.5063910417215 \tabularnewline
14 & 250 & 277.848145163016 & -27.8481451630157 \tabularnewline
15 & 312 & 252.439998947998 & 59.5600010520023 \tabularnewline
16 & 331 & 306.781471474710 & 24.2185285252905 \tabularnewline
17 & 256 & 328.878020824086 & -72.8780208240856 \tabularnewline
18 & 247 & 262.38542686064 & -15.3854268606401 \tabularnewline
19 & 291 & 248.348040421892 & 42.6519595781081 \tabularnewline
20 & 318 & 287.262920352813 & 30.7370796471873 \tabularnewline
21 & 296 & 315.30687837324 & -19.3068783732404 \tabularnewline
22 & 291 & 297.691630183772 & -6.69163018377213 \tabularnewline
23 & 313 & 291.586307293115 & 21.4136927068852 \tabularnewline
24 & 311 & 311.123774945452 & -0.123774945451771 \tabularnewline
25 & 273 & 311.010844913904 & -38.0108449139044 \tabularnewline
26 & 258 & 276.330434435023 & -18.3304344350232 \tabularnewline
27 & 361 & 259.606076113004 & 101.393923886996 \tabularnewline
28 & 391 & 352.11606657573 & 38.8839334242696 \tabularnewline
29 & 446 & 387.593067290699 & 58.4069327093006 \tabularnewline
30 & 433 & 440.882501023597 & -7.8825010235966 \tabularnewline
31 & 449 & 433.690649021419 & 15.3093509785812 \tabularnewline
32 & 479 & 447.658625195193 & 31.3413748048066 \tabularnewline
33 & 460 & 476.253931236537 & -16.2539312365374 \tabularnewline
34 & 466 & 461.424137043448 & 4.57586295655165 \tabularnewline
35 & 410 & 465.599072012344 & -55.5990720123438 \tabularnewline
36 & 415 & 414.87147982121 & 0.128520178789643 \tabularnewline
37 & 382 & 414.988739318213 & -32.9887393182129 \tabularnewline
38 & 409 & 384.890407557165 & 24.109592442835 \tabularnewline
39 & 496 & 406.887565586404 & 89.112434413596 \tabularnewline
40 & 471 & 488.192146193225 & -17.1921461932245 \tabularnewline
41 & 488 & 472.506341567086 & 15.4936584329142 \tabularnewline
42 & 584 & 486.642476543567 & 97.357523456433 \tabularnewline
43 & 610 & 575.469727932586 & 34.5302720674139 \tabularnewline
44 & 684 & 606.974526417276 & 77.0254735827239 \tabularnewline
45 & 626 & 677.251181598964 & -51.2511815989643 \tabularnewline
46 & 580 & 630.490526333193 & -50.4905263331933 \tabularnewline
47 & 444 & 584.423879235607 & -140.423879235607 \tabularnewline
48 & 552 & 456.303660283403 & 95.696339716597 \tabularnewline
49 & 473 & 543.615277539352 & -70.6152775393518 \tabularnewline
50 & 431 & 479.187169806103 & -48.187169806103 \tabularnewline
51 & 513 & 435.222063729761 & 77.7779362702393 \tabularnewline
52 & 467 & 506.185252318748 & -39.1852523187485 \tabularnewline
53 & 470 & 470.433333669984 & -0.43333366998354 \tabularnewline
54 & 455 & 470.037967832066 & -15.0379678320658 \tabularnewline
55 & 406 & 456.317596754666 & -50.3175967546663 \tabularnewline
56 & 424 & 410.408727490771 & 13.5912725092294 \tabularnewline
57 & 406 & 422.809159804707 & -16.8091598047072 \tabularnewline
58 & 373 & 407.472785063426 & -34.4727850634261 \tabularnewline
59 & 332 & 376.020436686068 & -44.0204366860677 \tabularnewline
60 & 310 & 335.856982882546 & -25.8569828825459 \tabularnewline
61 & 301 & 312.265537279502 & -11.2655372795024 \tabularnewline
62 & 296 & 301.987063912146 & -5.98706391214597 \tabularnewline
63 & 333 & 296.52457460135 & 36.4754253986498 \tabularnewline
64 & 374 & 329.804095961168 & 44.1959040388325 \tabularnewline
65 & 422 & 370.127643017899 & 51.8723569821008 \tabularnewline
66 & 424 & 417.455047518404 & 6.54495248159577 \tabularnewline
67 & 341 & 423.426544314664 & -82.4265443146642 \tabularnewline
68 & 216 & 348.222049448448 & -132.222049448448 \tabularnewline
69 & 319 & 227.585032312485 & 91.4149676875148 \tabularnewline
70 & 383 & 310.990402819179 & 72.0095971808209 \tabularnewline
71 & 360 & 376.690662687284 & -16.6906626872842 \tabularnewline
72 & 400 & 361.462402582289 & 38.5375974177108 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13324&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]265[/C][C]214[/C][C]51[/C][/ROW]
[ROW][C]4[/C][C]290[/C][C]260.531481697634[/C][C]29.4685183023661[/C][/ROW]
[ROW][C]5[/C][C]287[/C][C]287.418027188672[/C][C]-0.418027188671942[/C][/ROW]
[ROW][C]6[/C][C]270[/C][C]287.036626708695[/C][C]-17.0366267086955[/C][/ROW]
[ROW][C]7[/C][C]263[/C][C]271.492715259968[/C][C]-8.49271525996835[/C][/ROW]
[ROW][C]8[/C][C]265[/C][C]263.744114775999[/C][C]1.25588522400096[/C][/ROW]
[ROW][C]9[/C][C]252[/C][C]264.889961840998[/C][C]-12.8899618409977[/C][/ROW]
[ROW][C]10[/C][C]281[/C][C]253.129392753006[/C][C]27.8706072469942[/C][/ROW]
[ROW][C]11[/C][C]259[/C][C]278.558032968995[/C][C]-19.5580329689951[/C][/ROW]
[ROW][C]12[/C][C]312[/C][C]260.713635848632[/C][C]51.286364151368[/C][/ROW]
[ROW][C]13[/C][C]275[/C][C]307.506391041722[/C][C]-32.5063910417215[/C][/ROW]
[ROW][C]14[/C][C]250[/C][C]277.848145163016[/C][C]-27.8481451630157[/C][/ROW]
[ROW][C]15[/C][C]312[/C][C]252.439998947998[/C][C]59.5600010520023[/C][/ROW]
[ROW][C]16[/C][C]331[/C][C]306.781471474710[/C][C]24.2185285252905[/C][/ROW]
[ROW][C]17[/C][C]256[/C][C]328.878020824086[/C][C]-72.8780208240856[/C][/ROW]
[ROW][C]18[/C][C]247[/C][C]262.38542686064[/C][C]-15.3854268606401[/C][/ROW]
[ROW][C]19[/C][C]291[/C][C]248.348040421892[/C][C]42.6519595781081[/C][/ROW]
[ROW][C]20[/C][C]318[/C][C]287.262920352813[/C][C]30.7370796471873[/C][/ROW]
[ROW][C]21[/C][C]296[/C][C]315.30687837324[/C][C]-19.3068783732404[/C][/ROW]
[ROW][C]22[/C][C]291[/C][C]297.691630183772[/C][C]-6.69163018377213[/C][/ROW]
[ROW][C]23[/C][C]313[/C][C]291.586307293115[/C][C]21.4136927068852[/C][/ROW]
[ROW][C]24[/C][C]311[/C][C]311.123774945452[/C][C]-0.123774945451771[/C][/ROW]
[ROW][C]25[/C][C]273[/C][C]311.010844913904[/C][C]-38.0108449139044[/C][/ROW]
[ROW][C]26[/C][C]258[/C][C]276.330434435023[/C][C]-18.3304344350232[/C][/ROW]
[ROW][C]27[/C][C]361[/C][C]259.606076113004[/C][C]101.393923886996[/C][/ROW]
[ROW][C]28[/C][C]391[/C][C]352.11606657573[/C][C]38.8839334242696[/C][/ROW]
[ROW][C]29[/C][C]446[/C][C]387.593067290699[/C][C]58.4069327093006[/C][/ROW]
[ROW][C]30[/C][C]433[/C][C]440.882501023597[/C][C]-7.8825010235966[/C][/ROW]
[ROW][C]31[/C][C]449[/C][C]433.690649021419[/C][C]15.3093509785812[/C][/ROW]
[ROW][C]32[/C][C]479[/C][C]447.658625195193[/C][C]31.3413748048066[/C][/ROW]
[ROW][C]33[/C][C]460[/C][C]476.253931236537[/C][C]-16.2539312365374[/C][/ROW]
[ROW][C]34[/C][C]466[/C][C]461.424137043448[/C][C]4.57586295655165[/C][/ROW]
[ROW][C]35[/C][C]410[/C][C]465.599072012344[/C][C]-55.5990720123438[/C][/ROW]
[ROW][C]36[/C][C]415[/C][C]414.87147982121[/C][C]0.128520178789643[/C][/ROW]
[ROW][C]37[/C][C]382[/C][C]414.988739318213[/C][C]-32.9887393182129[/C][/ROW]
[ROW][C]38[/C][C]409[/C][C]384.890407557165[/C][C]24.109592442835[/C][/ROW]
[ROW][C]39[/C][C]496[/C][C]406.887565586404[/C][C]89.112434413596[/C][/ROW]
[ROW][C]40[/C][C]471[/C][C]488.192146193225[/C][C]-17.1921461932245[/C][/ROW]
[ROW][C]41[/C][C]488[/C][C]472.506341567086[/C][C]15.4936584329142[/C][/ROW]
[ROW][C]42[/C][C]584[/C][C]486.642476543567[/C][C]97.357523456433[/C][/ROW]
[ROW][C]43[/C][C]610[/C][C]575.469727932586[/C][C]34.5302720674139[/C][/ROW]
[ROW][C]44[/C][C]684[/C][C]606.974526417276[/C][C]77.0254735827239[/C][/ROW]
[ROW][C]45[/C][C]626[/C][C]677.251181598964[/C][C]-51.2511815989643[/C][/ROW]
[ROW][C]46[/C][C]580[/C][C]630.490526333193[/C][C]-50.4905263331933[/C][/ROW]
[ROW][C]47[/C][C]444[/C][C]584.423879235607[/C][C]-140.423879235607[/C][/ROW]
[ROW][C]48[/C][C]552[/C][C]456.303660283403[/C][C]95.696339716597[/C][/ROW]
[ROW][C]49[/C][C]473[/C][C]543.615277539352[/C][C]-70.6152775393518[/C][/ROW]
[ROW][C]50[/C][C]431[/C][C]479.187169806103[/C][C]-48.187169806103[/C][/ROW]
[ROW][C]51[/C][C]513[/C][C]435.222063729761[/C][C]77.7779362702393[/C][/ROW]
[ROW][C]52[/C][C]467[/C][C]506.185252318748[/C][C]-39.1852523187485[/C][/ROW]
[ROW][C]53[/C][C]470[/C][C]470.433333669984[/C][C]-0.43333366998354[/C][/ROW]
[ROW][C]54[/C][C]455[/C][C]470.037967832066[/C][C]-15.0379678320658[/C][/ROW]
[ROW][C]55[/C][C]406[/C][C]456.317596754666[/C][C]-50.3175967546663[/C][/ROW]
[ROW][C]56[/C][C]424[/C][C]410.408727490771[/C][C]13.5912725092294[/C][/ROW]
[ROW][C]57[/C][C]406[/C][C]422.809159804707[/C][C]-16.8091598047072[/C][/ROW]
[ROW][C]58[/C][C]373[/C][C]407.472785063426[/C][C]-34.4727850634261[/C][/ROW]
[ROW][C]59[/C][C]332[/C][C]376.020436686068[/C][C]-44.0204366860677[/C][/ROW]
[ROW][C]60[/C][C]310[/C][C]335.856982882546[/C][C]-25.8569828825459[/C][/ROW]
[ROW][C]61[/C][C]301[/C][C]312.265537279502[/C][C]-11.2655372795024[/C][/ROW]
[ROW][C]62[/C][C]296[/C][C]301.987063912146[/C][C]-5.98706391214597[/C][/ROW]
[ROW][C]63[/C][C]333[/C][C]296.52457460135[/C][C]36.4754253986498[/C][/ROW]
[ROW][C]64[/C][C]374[/C][C]329.804095961168[/C][C]44.1959040388325[/C][/ROW]
[ROW][C]65[/C][C]422[/C][C]370.127643017899[/C][C]51.8723569821008[/C][/ROW]
[ROW][C]66[/C][C]424[/C][C]417.455047518404[/C][C]6.54495248159577[/C][/ROW]
[ROW][C]67[/C][C]341[/C][C]423.426544314664[/C][C]-82.4265443146642[/C][/ROW]
[ROW][C]68[/C][C]216[/C][C]348.222049448448[/C][C]-132.222049448448[/C][/ROW]
[ROW][C]69[/C][C]319[/C][C]227.585032312485[/C][C]91.4149676875148[/C][/ROW]
[ROW][C]70[/C][C]383[/C][C]310.990402819179[/C][C]72.0095971808209[/C][/ROW]
[ROW][C]71[/C][C]360[/C][C]376.690662687284[/C][C]-16.6906626872842[/C][/ROW]
[ROW][C]72[/C][C]400[/C][C]361.462402582289[/C][C]38.5375974177108[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13324&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13324&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
326521451
4290260.53148169763429.4685183023661
5287287.418027188672-0.418027188671942
6270287.036626708695-17.0366267086955
7263271.492715259968-8.49271525996835
8265263.7441147759991.25588522400096
9252264.889961840998-12.8899618409977
10281253.12939275300627.8706072469942
11259278.558032968995-19.5580329689951
12312260.71363584863251.286364151368
13275307.506391041722-32.5063910417215
14250277.848145163016-27.8481451630157
15312252.43999894799859.5600010520023
16331306.78147147471024.2185285252905
17256328.878020824086-72.8780208240856
18247262.38542686064-15.3854268606401
19291248.34804042189242.6519595781081
20318287.26292035281330.7370796471873
21296315.30687837324-19.3068783732404
22291297.691630183772-6.69163018377213
23313291.58630729311521.4136927068852
24311311.123774945452-0.123774945451771
25273311.010844913904-38.0108449139044
26258276.330434435023-18.3304344350232
27361259.606076113004101.393923886996
28391352.1160665757338.8839334242696
29446387.59306729069958.4069327093006
30433440.882501023597-7.8825010235966
31449433.69064902141915.3093509785812
32479447.65862519519331.3413748048066
33460476.253931236537-16.2539312365374
34466461.4241370434484.57586295655165
35410465.599072012344-55.5990720123438
36415414.871479821210.128520178789643
37382414.988739318213-32.9887393182129
38409384.89040755716524.109592442835
39496406.88756558640489.112434413596
40471488.192146193225-17.1921461932245
41488472.50634156708615.4936584329142
42584486.64247654356797.357523456433
43610575.46972793258634.5302720674139
44684606.97452641727677.0254735827239
45626677.251181598964-51.2511815989643
46580630.490526333193-50.4905263331933
47444584.423879235607-140.423879235607
48552456.30366028340395.696339716597
49473543.615277539352-70.6152775393518
50431479.187169806103-48.187169806103
51513435.22206372976177.7779362702393
52467506.185252318748-39.1852523187485
53470470.433333669984-0.43333366998354
54455470.037967832066-15.0379678320658
55406456.317596754666-50.3175967546663
56424410.40872749077113.5912725092294
57406422.809159804707-16.8091598047072
58373407.472785063426-34.4727850634261
59332376.020436686068-44.0204366860677
60310335.856982882546-25.8569828825459
61301312.265537279502-11.2655372795024
62296301.987063912146-5.98706391214597
63333296.5245746013536.4754253986498
64374329.80409596116844.1959040388325
65422370.12764301789951.8723569821008
66424417.4550475184046.54495248159577
67341423.426544314664-82.4265443146642
68216348.222049448448-132.222049448448
69319227.58503231248591.4149676875148
70383310.99040281917972.0095971808209
71360376.690662687284-16.6906626872842
72400361.46240258228938.5375974177108







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73396.623412560975298.628073375495494.618751746456
74396.623412560975263.969394519808529.277430602143
75396.623412560975236.651257162433556.595567959518
76396.623412560975213.361052805230579.885772316721
77396.623412560975192.713887271858600.532937850093
78396.623412560975173.973246371901619.27357875005
79396.623412560975156.691967134555636.554857987396
80396.623412560975140.574392830768652.672432291183
81396.623412560975125.412973039947667.833852082003
82396.623412560975111.055374248600682.19145087335
83396.62341256097597.3858706215203695.86095450043
84396.62341256097584.3140971277721708.932727994179

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
73 & 396.623412560975 & 298.628073375495 & 494.618751746456 \tabularnewline
74 & 396.623412560975 & 263.969394519808 & 529.277430602143 \tabularnewline
75 & 396.623412560975 & 236.651257162433 & 556.595567959518 \tabularnewline
76 & 396.623412560975 & 213.361052805230 & 579.885772316721 \tabularnewline
77 & 396.623412560975 & 192.713887271858 & 600.532937850093 \tabularnewline
78 & 396.623412560975 & 173.973246371901 & 619.27357875005 \tabularnewline
79 & 396.623412560975 & 156.691967134555 & 636.554857987396 \tabularnewline
80 & 396.623412560975 & 140.574392830768 & 652.672432291183 \tabularnewline
81 & 396.623412560975 & 125.412973039947 & 667.833852082003 \tabularnewline
82 & 396.623412560975 & 111.055374248600 & 682.19145087335 \tabularnewline
83 & 396.623412560975 & 97.3858706215203 & 695.86095450043 \tabularnewline
84 & 396.623412560975 & 84.3140971277721 & 708.932727994179 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=13324&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]73[/C][C]396.623412560975[/C][C]298.628073375495[/C][C]494.618751746456[/C][/ROW]
[ROW][C]74[/C][C]396.623412560975[/C][C]263.969394519808[/C][C]529.277430602143[/C][/ROW]
[ROW][C]75[/C][C]396.623412560975[/C][C]236.651257162433[/C][C]556.595567959518[/C][/ROW]
[ROW][C]76[/C][C]396.623412560975[/C][C]213.361052805230[/C][C]579.885772316721[/C][/ROW]
[ROW][C]77[/C][C]396.623412560975[/C][C]192.713887271858[/C][C]600.532937850093[/C][/ROW]
[ROW][C]78[/C][C]396.623412560975[/C][C]173.973246371901[/C][C]619.27357875005[/C][/ROW]
[ROW][C]79[/C][C]396.623412560975[/C][C]156.691967134555[/C][C]636.554857987396[/C][/ROW]
[ROW][C]80[/C][C]396.623412560975[/C][C]140.574392830768[/C][C]652.672432291183[/C][/ROW]
[ROW][C]81[/C][C]396.623412560975[/C][C]125.412973039947[/C][C]667.833852082003[/C][/ROW]
[ROW][C]82[/C][C]396.623412560975[/C][C]111.055374248600[/C][C]682.19145087335[/C][/ROW]
[ROW][C]83[/C][C]396.623412560975[/C][C]97.3858706215203[/C][C]695.86095450043[/C][/ROW]
[ROW][C]84[/C][C]396.623412560975[/C][C]84.3140971277721[/C][C]708.932727994179[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=13324&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=13324&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
73396.623412560975298.628073375495494.618751746456
74396.623412560975263.969394519808529.277430602143
75396.623412560975236.651257162433556.595567959518
76396.623412560975213.361052805230579.885772316721
77396.623412560975192.713887271858600.532937850093
78396.623412560975173.973246371901619.27357875005
79396.623412560975156.691967134555636.554857987396
80396.623412560975140.574392830768652.672432291183
81396.623412560975125.412973039947667.833852082003
82396.623412560975111.055374248600682.19145087335
83396.62341256097597.3858706215203695.86095450043
84396.62341256097584.3140971277721708.932727994179



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = multiplicative ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=0, beta=0)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=0)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')